A 3.0kg- block sits on top of a 5.0kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force as shown in the figure . The coefficient of static friction between all surfaces is 0.65 and the kinetic coefficient is 0.42.
PART A: What is the minimum value of needed to move the two blocks?
PART B: If the force is 10% greater than your answer for (a), what is the acceleration of each block?
To find the minimum force needed to move the two blocks, we need to consider the forces acting on them and determine when the force of static friction is overcome.
PART A:
1. First, let's identify the forces acting on the blocks:
- The weight of the 3.0kg block (Force 1)
- The weight of the 5.0kg block (Force 2)
- The normal force acting on the 5.0kg block (Force 3)
- The force applied to the 5.0kg block pulling it to the right (Force 4)
- The force of static friction between the two blocks (Force 5)
2. We can calculate the force of static friction using the equation:
Force of static friction = coefficient of static friction * normal force
3. The normal force can be calculated by multiplying the mass of the 5.0kg block by the acceleration due to gravity:
Normal force = mass * acceleration due to gravity
4. Since the blocks are not moving, the force applied to the 5.0kg block must be equal to the force of static friction:
Force 4 = Force 5
5. To find the minimum force needed to move the two blocks, we need to increase the pulling force until it matches the maximum force of static friction. The maximum force of static friction can be calculated as:
Maximum force of static friction = coefficient of static friction * normal force
6. Therefore, the minimum force needed to move the two blocks is the maximum force of static friction.
PART B:
1. If the applied force is 10% greater than the minimum force calculated in Part A, the total force acting on the system is increased.
2. To determine the acceleration of each block, we need to consider the net force acting on each block individually.
3. For the 3.0kg block, the net force is the applied force minus the force of kinetic friction (since the blocks are now in motion). The force of kinetic friction can be calculated as:
Force of kinetic friction = coefficient of kinetic friction * normal force
4. For the 5.0kg block, the net force is the applied force minus the force of static friction, as the block is still stationary until the force of static friction is overcome.
5. Using Newton's second law (F = ma), we can calculate the acceleration of each block by dividing the net force acting on the block by its mass:
acceleration = net force / mass
By following these steps, you can find the minimum force needed to move the two blocks (Part A) and the acceleration of each block if the force is increased by 10% (Part B).